To find the standard deviation [tex]\(\sigma\)[/tex] of the given data, we start with the variance, which is provided. Variance [tex]\(\sigma^2\)[/tex] is a measure of the dispersion of the data points around the mean.
We are given:
[tex]\[
\text{Variance} \left(\sigma^2\right) = 159
\][/tex]
The standard deviation [tex]\(\sigma\)[/tex] is the square root of the variance. This can be expressed mathematically as:
[tex]\[
\sigma = \sqrt{\sigma^2}
\][/tex]
Now, substituting the given variance into the equation:
[tex]\[
\sigma = \sqrt{159}
\][/tex]
By evaluating the square root of 159, we get:
[tex]\[
\sigma \approx 12.609520212918492
\][/tex]
After calculating the standard deviation, we need to round it to the nearest tenth. By rounding 12.609520212918492 to one decimal place, we get:
[tex]\[
\sigma \approx 12.6
\][/tex]
So, the standard deviation [tex]\(\sigma\)[/tex] of the data, rounded to the nearest tenth, is:
[tex]\[
\sigma = 12.6
\][/tex]
